*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid and
even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
And, have you done the basic investigation to find out how much of conventional logic you invalidate with that change?
Note, that it may be hard to define "necessary consequence" in a formal matter.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its conclusion, so doesn't actually cause problems in normal logic (can you
show a case where it does?)
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there are
some statements we don't know if they CAN be sometimes true, so your
logic system would seem to not allow doing logic with that sort of
statement.
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid and
even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually means
before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional statement. It has no conclusion].
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
And that differs from the standard definition how exactly? Unless you
have some special personal meaning for 'necessary consequence' it would
appear to be simply a paraphrase of the definition you cite above.
André
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually means
before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not a
case of the conclusion is true and the premises are false, thus meets
the above validity criteria.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And that differs from the standard definition how exactly? Unless you
have some special personal meaning for 'necessary consequence' it would
Semantic relevance is a key aspect of 'necessary consequence'.
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not a
case of the conclusion is true and the premises are false, thus meets
the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of green cheese. An argument is valid if there is no truth *assignment* under
which the premises are true and the conclusion is false. The actual
truth values of these expressions don't play a role in the definition of validity.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And that differs from the standard definition how exactly? Unless you
have some special personal meaning for 'necessary consequence' it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And, have you done the basic investigation to find out how much of
conventional logic you invalidate with that change?
It categorically changes everything that is broken.
Note, that it may be hard to define "necessary consequence" in a
formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to {A,B} to derive C.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its
conclusion, so doesn't actually cause problems in normal logic (can
you show a case where it does?)
With my correction true and unprovable is impossible, unprovable simply
means untrue.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there
are some statements we don't know if they CAN be sometimes true, so
your logic system would seem to not allow doing logic with that sort
of statement.
An analytic statement is only known to be true when it is derived by
applying only truth preserving operations to all of its premises and all
of its premises are known to be true, otherwise its truth value is unknown.
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And, have you done the basic investigation to find out how much of
conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and start over?
I think, especially with the comment below, people will decide that your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a
formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to {A,B}
to derive C.
And what do you define truth perserving as?
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green cheese
then ll dogs are cats" IS Truth Preserving, since any time the premise
is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its
conclusion, so doesn't actually cause problems in normal logic (can
you show a case where it does?)
With my correction true and unprovable is impossible, unprovable
simply means untrue.
Ok, then you have just stated that your new logic system can't handle mathematics, and thus "Computer SCience" no longer exists as a logical system.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there
are some statements we don't know if they CAN be sometimes true, so
your logic system would seem to not allow doing logic with that sort
of statement.
An analytic statement is only known to be true when it is derived by
applying only truth preserving operations to all of its premises and
all of its premises are known to be true, otherwise its truth value is
unknown.
KNOWN to be True, not IS TRUE.
Your statement even admits that truth value might be unknow, which might allow it to even be UNKNOWABLE (maybe just in that system) if it can't
be proven or refuted.
There is NOTHING about an analytic statement that says it can only be
true if it is provable. Note, "its truth value is unknown" doesn't mean
it doesn't have a truth value, just that we don't know what that value is.
You are confusing Knowledge with Truth.
Your whole system is built on a Category Error.
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not
a case of the conclusion is true and the premises are false, thus
meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And that differs from the standard definition how exactly? Unless
you have some special personal meaning for 'necessary consequence'
it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of https://en.wikipedia.org/wiki/Categorical_proposition
On 2022-05-13 13:11, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not
a case of the conclusion is true and the premises are false, thus
meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Abstractions are designed to cover a large number of different cases. A concrete example cannot capture an abstraction.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
Into a concrete example of the issue that it corrects, quite yet.
Are you acknowledging that you haven't the foggiest idea what 'valid'
means? If you're trying to say more than this, I fail to see what it
might be.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.
And that differs from the standard definition how exactly? Unless
you have some special personal meaning for 'necessary consequence'
it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition
How exactly do two wikipedia articles provide a definition of 'semantic relevance' when neither article contains the word 'semantic' nor the
word 'relevance'?
André
On 5/13/2022 2:20 PM, André G. Isaak wrote:
On 2022-05-13 13:11, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
the conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a
conditional statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is
not a case of the conclusion is true and the premises are false,
thus meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Abstractions are designed to cover a large number of different cases.
A concrete example cannot capture an abstraction.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
Into a concrete example of the issue that it corrects, quite yet.
Are you acknowledging that you haven't the foggiest idea what 'valid'
means? If you're trying to say more than this, I fail to see what it
might be.
I am saying that I am redefining the concept of logical validity to
eliminate its divergence from correct reasoning.
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not
a case of the conclusion is true and the premises are false, thus
meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And that differs from the standard definition how exactly? Unless
you have some special personal meaning for 'necessary consequence'
it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of https://en.wikipedia.org/wiki/Categorical_proposition
On 2022-05-13 13:51, olcott wrote:
On 5/13/2022 2:20 PM, André G. Isaak wrote:
On 2022-05-13 13:11, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically >>>>>>>> unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>> means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a
conditional statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is
not a case of the conclusion is true and the premises are false,
thus meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth
*assignment* under which the premises are true and the conclusion
is false. The actual truth values of these expressions don't play a
role in the definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Abstractions are designed to cover a large number of different cases.
A concrete example cannot capture an abstraction.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
Into a concrete example of the issue that it corrects, quite yet.
Are you acknowledging that you haven't the foggiest idea what 'valid'
means? If you're trying to say more than this, I fail to see what it
might be.
I am saying that I am redefining the concept of logical validity to
eliminate its divergence from correct reasoning.
Except you haven't show any instances where it diverges from 'correct reasoning'.
You gave an example argument which was *not* valid, claimed
that it was valid and that this "fact" was somehow a problem. The only problem I can see is your failure to grasp what it means for something
to be valid.
If you can't even figure out whether an argument is valid or not, you're
not in any position to claim there is something wrong with the accepted concept of validity.
André
On 5/13/22 3:11 PM, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is not
a case of the conclusion is true and the premises are false, thus
meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.
And that differs from the standard definition how exactly? Unless
you have some special personal meaning for 'necessary consequence'
it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition
My first thought is that if you are going to be limiting your reasoning capability to simple things. You seem to be stuck in using simple logic methods, which will limit what you can actually prove.
What you don't seem to understand is that much of what we have logically proven, is based on higher order logical systems, which these simple
forms just can't handle.
In particular, Computation theory, like much of mathematics, needs
second order (or higher) logic forms, which the simple logic just can't handle.
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
And, have you done the basic investigation to find out how much of
conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and start
over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.
I think, especially with the comment below, people will decide that
your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a
formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to {A,B}
to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green
cheese then ll dogs are cats" IS Truth Preserving, since any time the
premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its
conclusion, so doesn't actually cause problems in normal logic (can
you show a case where it does?)
With my correction true and unprovable is impossible, unprovable
simply means untrue.
Ok, then you have just stated that your new logic system can't handle
mathematics, and thus "Computer SCience" no longer exists as a logical
system.
It corrects the divergence of classical and symbolic logic from correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there
are some statements we don't know if they CAN be sometimes true, so
your logic system would seem to not allow doing logic with that sort
of statement.
An analytic statement is only known to be true when it is derived by
applying only truth preserving operations to all of its premises and
all of its premises are known to be true, otherwise its truth value
is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
Your statement even admits that truth value might be unknow, which
might allow it to even be UNKNOWABLE (maybe just in that system) if it
can't be proven or refuted.
unprovable in the system means untrue in the system.
There is NOTHING about an analytic statement that says it can only be
true if it is provable. Note, "its truth value is unknown" doesn't
mean it doesn't have a truth value, just that we don't know what that
value is.
Within any formal system unprovable in the system means untrue in the
system.
The entire body of analytic truth is constructed only on the basis of semantic connections between expressions of language, or expressions
that are stipulated to have the semantic property of Boolean true.
Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then both of these factors that make an expression true also make it provable.
You are confusing Knowledge with Truth.
Your whole system is built on a Category Error.
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a
form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive argument
is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is valid
and even though premises and conclusion are semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
And, have you done the basic investigation to find out how much of conventional logic you invalidate with that change?
Note, that it may be hard to define "necessary consequence" in a formal matter.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its conclusion, so doesn't actually cause problems in normal logic (can you
show a case where it does?)
Note, that at least by some meanings of your words, it could beJeff Barnett
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there are
some statements we don't know if they CAN be sometimes true, so your
logic system would seem to not allow doing logic with that sort of statement.--
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.
And, have you done the basic investigation to find out how much of
conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and start
over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of its
premises.
I think, especially with the comment below, people will decide that
your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a
formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to {A,B} >>>> to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green
cheese then ll dogs are cats" IS Truth Preserving, since any time the
premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its
conclusion, so doesn't actually cause problems in normal logic (can
you show a case where it does?)
With my correction true and unprovable is impossible, unprovable
simply means untrue.
Ok, then you have just stated that your new logic system can't handle
mathematics, and thus "Computer SCience" no longer exists as a
logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there
are some statements we don't know if they CAN be sometimes true, so
your logic system would seem to not allow doing logic with that
sort of statement.
An analytic statement is only known to be true when it is derived by
applying only truth preserving operations to all of its premises and
all of its premises are known to be true, otherwise its truth value
is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, which
might allow it to even be UNKNOWABLE (maybe just in that system) if
it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
We know that there is a number that solves an equation, but we don't
know that number, or how to compute that number.
Can we say that it is true that such a number exists?
This means that we can define the floor of that number, which will be an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue' since
we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can only be
true if it is provable. Note, "its truth value is unknown" doesn't
mean it doesn't have a truth value, just that we don't know what that
value is.
Within any formal system unprovable in the system means untrue in the
system.
The entire body of analytic truth is constructed only on the basis of
semantic connections between expressions of language, or expressions
that are stipulated to have the semantic property of Boolean true.
Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then both
of these factors that make an expression true also make it provable.
You clearly are just stating words by rote and not actually
understanding them.
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are not provable.
You are making a Category Error in you logic system, and confusing
Knowledge with Truth.
You are confusing Knowledge with Truth.
Your whole system is built on a Category Error.
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
the conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.
And, have you done the basic investigation to find out how much of >>>>>> conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and start
over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
I think, especially with the comment below, people will decide that
your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a
formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to
{A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green
cheese then ll dogs are cats" IS Truth Preserving, since any time
the premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its >>>>>> conclusion, so doesn't actually cause problems in normal logic
(can you show a case where it does?)
With my correction true and unprovable is impossible, unprovable
simply means untrue.
Ok, then you have just stated that your new logic system can't
handle mathematics, and thus "Computer SCience" no longer exists as
a logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument,
and arguement whose premises can at least some times be true, but
there are some statements we don't know if they CAN be sometimes
true, so your logic system would seem to not allow doing logic
with that sort of statement.
An analytic statement is only known to be true when it is derived
by applying only truth preserving operations to all of its premises
and all of its premises are known to be true, otherwise its truth
value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, which
might allow it to even be UNKNOWABLE (maybe just in that system) if
it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
We know that there is a number that solves an equation, but we don't
know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has been stipulated in your deinitions.
This means that we can define the floor of that number, which will be
an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue'
since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can only
be true if it is provable. Note, "its truth value is unknown"
doesn't mean it doesn't have a truth value, just that we don't know
what that value is.
Within any formal system unprovable in the system means untrue in the
system.
The entire body of analytic truth is constructed only on the basis of
semantic connections between expressions of language, or expressions
that are stipulated to have the semantic property of Boolean true.
Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then both
of these factors that make an expression true also make it provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1) or
the consequences of (2).
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are not
provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the sense organs to verify their truth.
You are making a Category Error in you logic system, and confusing
Knowledge with Truth.
You are confusing Knowledge with Truth.
Your whole system is built on a Category Error.
On 5/13/2022 3:03 PM, Richard Damon wrote:
On 5/13/22 3:11 PM, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
the conclusion nevertheless to be false. Otherwise, a deductive
argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically
unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually
means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a
conditional statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is
not a case of the conclusion is true and the premises are false,
thus meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity.
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth *assignment*
under which the premises are true and the conclusion is false. The
actual truth values of these expressions don't play a role in the
definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.
And that differs from the standard definition how exactly? Unless
you have some special personal meaning for 'necessary consequence' >>>>>> it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition
My first thought is that if you are going to be limiting your
reasoning capability to simple things. You seem to be stuck in using
simple logic methods, which will limit what you can actually prove.
Not when all of natural language semantics has been fully formalized and directly integrated into its own formal system.
What you don't seem to understand is that much of what we have
logically proven, is based on higher order logical systems, which
these simple forms just can't handle.
In particular, Computation theory, like much of mathematics, needs
second order (or higher) logic forms, which the simple logic just
can't handle.
I created Minimal Type Theory to express HOL using very slightly adapted syntax of FOL. In an early version of MTT it translated its expressions
into directed graphs so that pathological self-reference could be seen
as infinite cycle in the di-graph.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically >>>>>>>> unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
all of its premises.
And, have you done the basic investigation to find out how much
of conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and
start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
I think, especially with the comment below, people will decide that
your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a >>>>>>> formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to
{A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green
cheese then ll dogs are cats" IS Truth Preserving, since any time
the premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove
its conclusion, so doesn't actually cause problems in normal
logic (can you show a case where it does?)
With my correction true and unprovable is impossible, unprovable
simply means untrue.
Ok, then you have just stated that your new logic system can't
handle mathematics, and thus "Computer SCience" no longer exists as
a logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument,
and arguement whose premises can at least some times be true, but >>>>>>> there are some statements we don't know if they CAN be sometimes >>>>>>> true, so your logic system would seem to not allow doing logic
with that sort of statement.
An analytic statement is only known to be true when it is derived
by applying only truth preserving operations to all of its
premises and all of its premises are known to be true, otherwise
its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, which
might allow it to even be UNKNOWABLE (maybe just in that system) if
it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE (not 'untrue').
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we don't
know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has been
stipulated in your deinitions.
This means that we can define the floor of that number, which will be
an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue'
since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can only
be true if it is provable. Note, "its truth value is unknown"
doesn't mean it doesn't have a truth value, just that we don't know
what that value is.
Within any formal system unprovable in the system means untrue in
the system.
The entire body of analytic truth is constructed only on the basis
of semantic connections between expressions of language, or
expressions that are stipulated to have the semantic property of
Boolean true. Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then
both of these factors that make an expression true also make it
provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are not
provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its
meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the
sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
True and unprovable become impossible because Provable() is an aspect of True().
On 5/13/22 4:14 PM, olcott wrote:
On 5/13/2022 3:03 PM, Richard Damon wrote:
On 5/13/22 3:11 PM, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is
valid and even though premises and conclusion are semantically >>>>>>>> unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>> means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a
conditional statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is
not a case of the conclusion is true and the premises are false,
thus meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth
*assignment* under which the premises are true and the conclusion
is false. The actual truth values of these expressions don't play a
role in the definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
all of its premises.
And that differs from the standard definition how exactly? Unless >>>>>>> you have some special personal meaning for 'necessary
consequence' it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition
My first thought is that if you are going to be limiting your
reasoning capability to simple things. You seem to be stuck in using
simple logic methods, which will limit what you can actually prove.
Not when all of natural language semantics has been fully formalized
and directly integrated into its own formal system.
Nope doesn't work. Remember, formal system are based on a finite, or
perhaps extended to countable, number of base axiom.
I think you basis is going to hit the problem that the number of natural language 'facts' you are entering into your system isn't so limited.
Having an uncountable number of axioms in your system breaks a lot of
thngs. In fact, I think it breaks the definition of 'provable' or 'refutable'.
What you don't seem to understand is that much of what we have
logically proven, is based on higher order logical systems, which
these simple forms just can't handle.
In particular, Computation theory, like much of mathematics, needs
second order (or higher) logic forms, which the simple logic just
can't handle.
I created Minimal Type Theory to express HOL using very slightly
adapted syntax of FOL. In an early version of MTT it translated its
expressions into directed graphs so that pathological self-reference
could be seen as infinite cycle in the di-graph.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
Again, the error you are going to run into is your system is now based
on an uncountable number of inital truths, so a lot of the rules for reasoning break down. This makes you system VERY prone to becoming inconsistent (if not a certainty).
There are problems when you allow uncountable infinites into your base
logic.
On 5/13/2022 4:30 PM, Richard Damon wrote:
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it
takes a form that makes it impossible for the premises to be >>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>> deductive argument is said to be invalid.
https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is >>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>> unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it
takes a form such that its conclusion is a necessary
consequence of all of its premises.
And, have you done the basic investigation to find out how much >>>>>>>> of conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and
start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
I think, especially with the comment below, people will decide
that your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in a >>>>>>>> formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to >>>>>>> {A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green
cheese then ll dogs are cats" IS Truth Preserving, since any time
the premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild >>>>>>>> inference by normal logic, can never be used to actually prove >>>>>>>> its conclusion, so doesn't actually cause problems in normal
logic (can you show a case where it does?)
With my correction true and unprovable is impossible, unprovable >>>>>>> simply means untrue.
Ok, then you have just stated that your new logic system can't
handle mathematics, and thus "Computer SCience" no longer exists
as a logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be >>>>>>>> construed that you only accept as a correct deductive argument, >>>>>>>> and arguement whose premises can at least some times be true,
but there are some statements we don't know if they CAN be
sometimes true, so your logic system would seem to not allow
doing logic with that sort of statement.
An analytic statement is only known to be true when it is derived >>>>>>> by applying only truth preserving operations to all of its
premises and all of its premises are known to be true, otherwise >>>>>>> its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, which >>>>>> might allow it to even be UNKNOWABLE (maybe just in that system)
if it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE
(not 'untrue').
Unprovable means untrue and does not mean false in Prolog.
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we don't
know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has been
stipulated in your deinitions.
This means that we can define the floor of that number, which will
be an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue'
since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can only >>>>>> be true if it is provable. Note, "its truth value is unknown"
doesn't mean it doesn't have a truth value, just that we don't
know what that value is.
Within any formal system unprovable in the system means untrue in
the system.
The entire body of analytic truth is constructed only on the basis
of semantic connections between expressions of language, or
expressions that are stipulated to have the semantic property of
Boolean true. Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then
both of these factors that make an expression true also make it
provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are
not provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its
meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the
sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
Try and provide an example of a possible truth that does not require one
of those two.
On 5/13/2022 4:39 PM, Richard Damon wrote:
On 5/13/22 4:14 PM, olcott wrote:
On 5/13/2022 3:03 PM, Richard Damon wrote:
On 5/13/22 3:11 PM, olcott wrote:
On 5/13/2022 2:00 PM, André G. Isaak wrote:
On 2022-05-13 12:50, olcott wrote:
On 5/13/2022 1:28 PM, André G. Isaak wrote:
On 2022-05-13 11:20, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it
takes a form that makes it impossible for the premises to be >>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>> deductive argument is said to be invalid.
https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is >>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>> unrelated.
That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>>> means before you attempt to "correct" the definition.
[Also, the above isn't even an argument. It is simply a
conditional statement. It has no conclusion].
(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.
Because the premises are false and the conclusion is false it is >>>>>>> not a case of the conclusion is true and the premises are false, >>>>>>> thus meets the above validity criteria.
No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>>
Logic has no concept of whether, for example, the moon is made of
green cheese. An argument is valid if there is no truth
*assignment* under which the premises are true and the conclusion
is false. The actual truth values of these expressions don't play
a role in the definition of validity.
I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.
Clearly I have not yet translated this abstraction:
A deductive argument is said to be valid if and only if it takes a
form such that its conclusion is a necessary consequence of all of
its premises.
Into a concrete example of the issue that it corrects, quite yet.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it
takes a form such that its conclusion is a necessary
consequence of all of its premises.
And that differs from the standard definition how exactly?
Unless you have some special personal meaning for 'necessary
consequence' it would
Semantic relevance is a key aspect of 'necessary consequence'.
Defined how exactly?
André
Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition
My first thought is that if you are going to be limiting your
reasoning capability to simple things. You seem to be stuck in using
simple logic methods, which will limit what you can actually prove.
Not when all of natural language semantics has been fully formalized
and directly integrated into its own formal system.
Nope doesn't work. Remember, formal system are based on a finite, or
perhaps extended to countable, number of base axiom.
I think you basis is going to hit the problem that the number of
natural language 'facts' you are entering into your system isn't so
limited.
Having an uncountable number of axioms in your system breaks a lot of
thngs. In fact, I think it breaks the definition of 'provable' or
'refutable'.
What you don't seem to understand is that much of what we have
logically proven, is based on higher order logical systems, which
these simple forms just can't handle.
In particular, Computation theory, like much of mathematics, needs
second order (or higher) logic forms, which the simple logic just
can't handle.
I created Minimal Type Theory to express HOL using very slightly
adapted syntax of FOL. In an early version of MTT it translated its
expressions into directed graphs so that pathological self-reference
could be seen as infinite cycle in the di-graph.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
Again, the error you are going to run into is your system is now based
on an uncountable number of inital truths, so a lot of the rules for
reasoning break down. This makes you system VERY prone to becoming
inconsistent (if not a certainty).
There are problems when you allow uncountable infinites into your base
logic.
Uncountable truths that are entirely comprised of different combinations
of countable constituent parts are evaluatable on the basis of these constituents that are later recombined back into the original expression.
On 5/13/22 5:53 PM, olcott wrote:
On 5/13/2022 4:30 PM, Richard Damon wrote:
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it >>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>>> deductive argument is said to be invalid.
https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is >>>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>>> unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it >>>>>>>>>> takes a form such that its conclusion is a necessary
consequence of all of its premises.
And, have you done the basic investigation to find out how much >>>>>>>>> of conventional logic you invalidate with that change?
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and
start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.
I think, especially with the comment below, people will decide
that your "new" logic systm isn't worth the cost to switch to.
Note, that it may be hard to define "necessary consequence" in >>>>>>>>> a formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>> {A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate True >>>>>>> Results (which means the statement "If the moon is made of green >>>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time >>>>>>> the premise is true (never) the conclusion is true.
It should be noted that your example, while considered an vaild >>>>>>>>> inference by normal logic, can never be used to actually prove >>>>>>>>> its conclusion, so doesn't actually cause problems in normal >>>>>>>>> logic (can you show a case where it does?)
With my correction true and unprovable is impossible, unprovable >>>>>>>> simply means untrue.
Ok, then you have just stated that your new logic system can't
handle mathematics, and thus "Computer SCience" no longer exists >>>>>>> as a logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people.
Note, that at least by some meanings of your words, it could be >>>>>>>>> construed that you only accept as a correct deductive argument, >>>>>>>>> and arguement whose premises can at least some times be true, >>>>>>>>> but there are some statements we don't know if they CAN be
sometimes true, so your logic system would seem to not allow >>>>>>>>> doing logic with that sort of statement.
An analytic statement is only known to be true when it is
derived by applying only truth preserving operations to all of >>>>>>>> its premises and all of its premises are known to be true,
otherwise its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow,
which might allow it to even be UNKNOWABLE (maybe just in that
system) if it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE
(not 'untrue').
Unprovable means untrue and does not mean false in Prolog.
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we
don't know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has been
stipulated in your deinitions.
This means that we can define the floor of that number, which will
be an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue'
since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can
only be true if it is provable. Note, "its truth value is
unknown" doesn't mean it doesn't have a truth value, just that we >>>>>>> don't know what that value is.
Within any formal system unprovable in the system means untrue in
the system.
The entire body of analytic truth is constructed only on the basis >>>>>> of semantic connections between expressions of language, or
expressions that are stipulated to have the semantic property of
Boolean true. Lacking both of these and the expression is untrue.
Since axioms are provable on the basis that they are axioms then
both of these factors that make an expression true also make it
provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to
(1) or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are
not provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its
meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the
sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
Try and provide an example of a possible truth that does not require
one of those two.
The result of applying the operation of replacing N by N/2 if N is even
or by 3N+1 if N is odd will eventually get you to the number 1 for all Natural numbers N > 0.
This statement MUST be either True or False, by its nature, there is no
other possible state.
This statement seems to be true, but it has unable to be proven to be true.
Yes, we can not validly USE the idea that this statement is true to
prove something else, because we know that it is still possible that it
won't be true. But we CAN use that it will either be true or false to
show something.
That is an analytical expression that isn't proven to be an analytical
truth, but it may still be true,
On 5/13/2022 5:14 PM, Richard Damon wrote:
On 5/13/22 5:53 PM, olcott wrote:
On 5/13/2022 4:30 PM, Richard Damon wrote:
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it >>>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, >>>>>>>>>>> a deductive argument is said to be invalid.
https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats is >>>>>>>>>>> valid and even though premises and conclusion are
semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it >>>>>>>>>>> takes a form such that its conclusion is a necessary
consequence of all of its premises.
And, have you done the basic investigation to find out how >>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and >>>>>>>> start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.
I think, especially with the comment below, people will decide >>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>
Note, that it may be hard to define "necessary consequence" in >>>>>>>>>> a formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>>> {A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate
True Results (which means the statement "If the moon is made of >>>>>>>> green cheese then ll dogs are cats" IS Truth Preserving, since >>>>>>>> any time the premise is true (never) the conclusion is true.
It should be noted that your example, while considered an
vaild inference by normal logic, can never be used to actually >>>>>>>>>> prove its conclusion, so doesn't actually cause problems in >>>>>>>>>> normal logic (can you show a case where it does?)
With my correction true and unprovable is impossible,
unprovable simply means untrue.
Ok, then you have just stated that your new logic system can't >>>>>>>> handle mathematics, and thus "Computer SCience" no longer exists >>>>>>>> as a logical system.
It corrects the divergence of classical and symbolic logic from
correct reasoning.
This makes you system not much more than a toy for most people. >>>>>>>>
Note, that at least by some meanings of your words, it could >>>>>>>>>> be construed that you only accept as a correct deductive
argument, and arguement whose premises can at least some times >>>>>>>>>> be true, but there are some statements we don't know if they >>>>>>>>>> CAN be sometimes true, so your logic system would seem to not >>>>>>>>>> allow doing logic with that sort of statement.
An analytic statement is only known to be true when it is
derived by applying only truth preserving operations to all of >>>>>>>>> its premises and all of its premises are known to be true,
otherwise its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow,
which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>> system) if it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE
(not 'untrue').
Unprovable means untrue and does not mean false in Prolog.
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we
don't know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has been
stipulated in your deinitions.
This means that we can define the floor of that number, which will >>>>>> be an integer (call it N), is it true that this number exists?
That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be 'untrue' >>>>>> since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can
only be true if it is provable. Note, "its truth value is
unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>> we don't know what that value is.
Within any formal system unprovable in the system means untrue in >>>>>>> the system.
The entire body of analytic truth is constructed only on the
basis of semantic connections between expressions of language, or >>>>>>> expressions that are stipulated to have the semantic property of >>>>>>> Boolean true. Lacking both of these and the expression is untrue. >>>>>>>
Since axioms are provable on the basis that they are axioms then >>>>>>> both of these factors that make an expression true also make it
provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to
(1) or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are
not provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its
meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the
sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
Try and provide an example of a possible truth that does not require
one of those two.
The result of applying the operation of replacing N by N/2 if N is
even or by 3N+1 if N is odd will eventually get you to the number 1
for all Natural numbers N > 0.
This statement MUST be either True or False, by its nature, there is
no other possible state.
This statement seems to be true, but it has unable to be proven to be
true.
Yes, we can not validly USE the idea that this statement is true to
prove something else, because we know that it is still possible that
it won't be true. But we CAN use that it will either be true or false
to show something.
That is an analytical expression that isn't proven to be an analytical
truth, but it may still be true,
Probably an unconscious strawman error, that does not contradict my
original claim because it is a strawman error.
True(x) iff Stipulated_True(x) or Proven_True(x)
I am referring to <is> true and you are referring to <might be> true,
they are not the same.
On 5/13/22 6:23 PM, olcott wrote:
On 5/13/2022 5:14 PM, Richard Damon wrote:
On 5/13/22 5:53 PM, olcott wrote:
On 5/13/2022 4:30 PM, Richard Damon wrote:
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it >>>>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, >>>>>>>>>>>> a deductive argument is said to be invalid.
https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats >>>>>>>>>>>> is valid and even though premises and conclusion are
semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it >>>>>>>>>>>> takes a form such that its conclusion is a necessary
consequence of all of its premises.
And, have you done the basic investigation to find out how >>>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>>
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and >>>>>>>>> start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
all of its premises.
I think, especially with the comment below, people will decide >>>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>>
Note, that it may be hard to define "necessary consequence" >>>>>>>>>>> in a formal matter.
{A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>>>> {A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate >>>>>>>>> True Results (which means the statement "If the moon is made of >>>>>>>>> green cheese then ll dogs are cats" IS Truth Preserving, since >>>>>>>>> any time the premise is true (never) the conclusion is true. >>>>>>>>>
It should be noted that your example, while considered an >>>>>>>>>>> vaild inference by normal logic, can never be used to
actually prove its conclusion, so doesn't actually cause >>>>>>>>>>> problems in normal logic (can you show a case where it does?) >>>>>>>>>>>
With my correction true and unprovable is impossible,
unprovable simply means untrue.
Ok, then you have just stated that your new logic system can't >>>>>>>>> handle mathematics, and thus "Computer SCience" no longer
exists as a logical system.
It corrects the divergence of classical and symbolic logic from >>>>>>>> correct reasoning.
This makes you system not much more than a toy for most people. >>>>>>>>>
Note, that at least by some meanings of your words, it could >>>>>>>>>>> be construed that you only accept as a correct deductive >>>>>>>>>>> argument, and arguement whose premises can at least some >>>>>>>>>>> times be true, but there are some statements we don't know if >>>>>>>>>>> they CAN be sometimes true, so your logic system would seem >>>>>>>>>>> to not allow doing logic with that sort of statement.
An analytic statement is only known to be true when it is
derived by applying only truth preserving operations to all of >>>>>>>>>> its premises and all of its premises are known to be true, >>>>>>>>>> otherwise its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, >>>>>>>>> which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>>> system) if it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE
(not 'untrue').
Unprovable means untrue and does not mean false in Prolog.
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we
don't know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has
been stipulated in your deinitions.
This means that we can define the floor of that number, which
will be an integer (call it N), is it true that this number exists? >>>>>>>
That interger, MUST be either even or odd, so we know that either >>>>>>> iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be
'untrue' since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can >>>>>>>>> only be true if it is provable. Note, "its truth value is
unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>>> we don't know what that value is.
Within any formal system unprovable in the system means untrue >>>>>>>> in the system.
The entire body of analytic truth is constructed only on the
basis of semantic connections between expressions of language, >>>>>>>> or expressions that are stipulated to have the semantic property >>>>>>>> of Boolean true. Lacking both of these and the expression is
untrue.
Since axioms are provable on the basis that they are axioms then >>>>>>>> both of these factors that make an expression true also make it >>>>>>>> provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression of >>>>>> language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to
(1) or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but it >>>>>>> accepts that there is OTHER things that happen to be true but are >>>>>>> not provable.
Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its
meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from the >>>>>> sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).
Try and provide an example of a possible truth that does not require
one of those two.
The result of applying the operation of replacing N by N/2 if N is
even or by 3N+1 if N is odd will eventually get you to the number 1
for all Natural numbers N > 0.
This statement MUST be either True or False, by its nature, there is
no other possible state.
This statement seems to be true, but it has unable to be proven to be
true.
Yes, we can not validly USE the idea that this statement is true to
prove something else, because we know that it is still possible that
it won't be true. But we CAN use that it will either be true or false
to show something.
That is an analytical expression that isn't proven to be an
analytical truth, but it may still be true,
Probably an unconscious strawman error, that does not contradict my
original claim because it is a strawman error.
True(x) iff Stipulated_True(x) or Proven_True(x)
I am referring to <is> true and you are referring to <might be> true,
they are not the same.
Then why dod you say "Possible truth", if you meant an ACTUAL truth.
How about;
x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1
True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
Proven Truth by your rules.
On 5/13/2022 6:14 PM, Richard Damon wrote:
On 5/13/22 6:23 PM, olcott wrote:
On 5/13/2022 5:14 PM, Richard Damon wrote:
On 5/13/22 5:53 PM, olcott wrote:
On 5/13/2022 4:30 PM, Richard Damon wrote:
On 5/13/22 4:56 PM, olcott wrote:
On 5/13/2022 3:43 PM, Richard Damon wrote:
On 5/13/22 3:43 PM, olcott wrote:
On 5/13/2022 2:13 PM, Richard Damon wrote:
On 5/13/22 2:10 PM, olcott wrote:
On 5/13/2022 12:47 PM, Richard Damon wrote:
On 5/13/22 1:20 PM, olcott wrote:
*Validity and Soundness*
A deductive argument is said to be valid if and only if it >>>>>>>>>>>>> takes a form that makes it impossible for the premises to >>>>>>>>>>>>> be true and the conclusion nevertheless to be false. >>>>>>>>>>>>> Otherwise, a deductive argument is said to be invalid. >>>>>>>>>>>>> https://iep.utm.edu/val-snd/
If the Moon is made of green cheese then all dogs are cats >>>>>>>>>>>>> is valid and even though premises and conclusion are >>>>>>>>>>>>> semantically unrelated.
*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it >>>>>>>>>>>>> takes a form such that its conclusion is a necessary >>>>>>>>>>>>> consequence of all of its premises.
And, have you done the basic investigation to find out how >>>>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>>>
It categorically changes everything that is broken.
So, you are saying we need to throw out EVERYTHING we know and >>>>>>>>>> start over?
Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it
takes a form such that its conclusion is a necessary
consequence of all of its premises.
I think, especially with the comment below, people will decide >>>>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>>>
Note, that it may be hard to define "necessary consequence" >>>>>>>>>>>> in a formal matter.
{A,B} ⊢ C only when truth preserving operations are applied >>>>>>>>>>> to {A,B} to derive C.
And what do you define truth perserving as?
Semantic relevance is maintained.
Normally the phrase means that True Premises always generate >>>>>>>>>> True Results (which means the statement "If the moon is made >>>>>>>>>> of green cheese then ll dogs are cats" IS Truth Preserving, >>>>>>>>>> since any time the premise is true (never) the conclusion is >>>>>>>>>> true.
It should be noted that your example, while considered an >>>>>>>>>>>> vaild inference by normal logic, can never be used to
actually prove its conclusion, so doesn't actually cause >>>>>>>>>>>> problems in normal logic (can you show a case where it does?) >>>>>>>>>>>>
With my correction true and unprovable is impossible,
unprovable simply means untrue.
Ok, then you have just stated that your new logic system can't >>>>>>>>>> handle mathematics, and thus "Computer SCience" no longer
exists as a logical system.
It corrects the divergence of classical and symbolic logic from >>>>>>>>> correct reasoning.
This makes you system not much more than a toy for most people. >>>>>>>>>>
Note, that at least by some meanings of your words, it could >>>>>>>>>>>> be construed that you only accept as a correct deductive >>>>>>>>>>>> argument, and arguement whose premises can at least some >>>>>>>>>>>> times be true, but there are some statements we don't know >>>>>>>>>>>> if they CAN be sometimes true, so your logic system would >>>>>>>>>>>> seem to not allow doing logic with that sort of statement. >>>>>>>>>>>>
An analytic statement is only known to be true when it is >>>>>>>>>>> derived by applying only truth preserving operations to all >>>>>>>>>>> of its premises and all of its premises are known to be true, >>>>>>>>>>> otherwise its truth value is unknown.
KNOWN to be True, not IS TRUE.
It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.
So, you don't know what is still valid to use?
Your statement even admits that truth value might be unknow, >>>>>>>>>> which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>>>> system) if it can't be proven or refuted.
unprovable in the system means untrue in the system.
And what does 'untrue' mean?
Untrue means the same thing as Prolog's negation as failure.
Which means... ?
Prolog, as I remember, ASSUMES that anything not provable is FALSE >>>>>> (not 'untrue').
Unprovable means untrue and does not mean false in Prolog.
There are only two possible ways that any analytical expression of
We know that there is a number that solves an equation, but we >>>>>>>> don't know that number, or how to compute that number.
Can we say that it is true that such a number exists?
If you defined your terms correctly, then yes because this has
been stipulated in your deinitions.
This means that we can define the floor of that number, which
will be an integer (call it N), is it true that this number exists? >>>>>>>>
That interger, MUST be either even or odd, so we know that
either iseven(N) is true or isodd(N) is true.
By your logic, the 'truth value' of both of those must be
'untrue' since we can not prove which one it is.
This is the sort of problem you run into with your system.
There is NOTHING about an analytic statement that says it can >>>>>>>>>> only be true if it is provable. Note, "its truth value is
unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>>>> we don't know what that value is.
Within any formal system unprovable in the system means untrue >>>>>>>>> in the system.
The entire body of analytic truth is constructed only on the >>>>>>>>> basis of semantic connections between expressions of language, >>>>>>>>> or expressions that are stipulated to have the semantic
property of Boolean true. Lacking both of these and the
expression is untrue.
Since axioms are provable on the basis that they are axioms
then both of these factors that make an expression true also >>>>>>>>> make it provable.
You clearly are just stating words by rote and not actually
understanding them.
There are only two possible ways that any analytical expression
of language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to >>>>>>> (1) or the consequences of (2).
So there exists an integer number N is neither Even or Odd? (it is >>>>>> untrue for both tests)
I don't think you actually understand what that means.
Analytic Truth is truth that is provable, that is correct, but >>>>>>>> it accepts that there is OTHER things that happen to be true but >>>>>>>> are not provable.
Analytic truth includes every expression of language that can be >>>>>>> completely verified as totally true entirely on the basis of its >>>>>>> meaning without requiring any sense data from the sense organs.
Empirical expressions of language also require sense data from
the sense organs to verify their truth.
You still don't understand, do you.
You still confuse Truth with Knowledge.
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1) >>>>> or the consequences of (2).
Try and provide an example of a possible truth that does not
require one of those two.
The result of applying the operation of replacing N by N/2 if N is
even or by 3N+1 if N is odd will eventually get you to the number 1
for all Natural numbers N > 0.
This statement MUST be either True or False, by its nature, there is
no other possible state.
This statement seems to be true, but it has unable to be proven to
be true.
Yes, we can not validly USE the idea that this statement is true to
prove something else, because we know that it is still possible that
it won't be true. But we CAN use that it will either be true or
false to show something.
That is an analytical expression that isn't proven to be an
analytical truth, but it may still be true,
Probably an unconscious strawman error, that does not contradict my
original claim because it is a strawman error.
True(x) iff Stipulated_True(x) or Proven_True(x)
I am referring to <is> true and you are referring to <might be> true,
they are not the same.
Then why dod you say "Possible truth", if you meant an ACTUAL truth.
My system rejects expressions of language that are impossibly true such
as expressions that are true and unprovable.
How about;
x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1
True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
Proven Truth by your rules.
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